Here is a chance to play a fractions version of the classic
Can you be the first to complete a row of three?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find out about Magic Squares in this article written for students. Why are they magic?!
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
An account of some magic squares and their properties and and how to construct them for yourself.
Find a great variety of ways of asking questions which make 8.
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Delight your friends with this cunning trick! Can you explain how
Can you explain how this card trick works?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
There are nasty versions of this dice game but we'll start with the nice ones...
Here is a chance to play a version of the classic Countdown Game.
This challenge extends the Plants investigation so now four or more children are involved.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
What are the missing numbers in the pyramids?
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This article for teachers suggests ideas for activities built around 10 and 2010.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Using the 8 dominoes make a square where each of the columns and
rows adds up to 8
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
How can we help students make sense of addition and subtraction of negative numbers?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
What is the sum of all the digits in all the integers from one to
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
How many solutions can you find to this sum? Each of the different letters stands for a different number.